Simplify the following expression: $ n = \dfrac{-9x - 1}{-5x} + \dfrac{-9}{2} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-9x - 1}{-5x} \times \dfrac{2}{2} = \dfrac{-18x - 2}{-10x} $ Multiply the second expression by $\dfrac{-5x}{-5x}$ $ \dfrac{-9}{2} \times \dfrac{-5x}{-5x} = \dfrac{45x}{-10x} $ Therefore $ n = \dfrac{-18x - 2}{-10x} + \dfrac{45x}{-10x} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-18x - 2 + 45x}{-10x} $ $n = \dfrac{27x - 2}{-10x}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{-27x + 2}{10x}$